Shaped curve by blending two circular arcs

Abstract

Segments of two given circular arcs can be blended to produce a segment of a new curve. The new curve that been produced which also known as blending curve is form in a C-shape. That’s mean the two circular arcs are blend at the same endpoints. Bezier Curve refer to [1] is the main application in this construction of blending curve. As the two circular arcs are create using the Rational Bezier Curve for the shape refer to [2]. First degree of Bezier Curve is use in blending function along with functionH(t). Blending can provide a smooth transition from one curve to another and can give various degrees of smoothness at the endpoints of the blend, where the smoothness is measured analogously to parametric continuity, Cn and geometric continuity, Gn. The accuracy of the approximation to a best blending curve obtained by different blending formulas is compared via analysis. Two types of blending formula introduced, which are Blend A and B. Blend A which involve only parametric continuity, C0, C1 and C2 Blend A. Next, new blending formula known as Blend B which actually a correction to the C0 Blend A. So, some correction term are added to the blending function in C0 Blend A for obtaining parametric continuity, C1 and C2 Blend B. Then, geometric continuity use for Blend B by increasing the smoothness of blending curve that result in parametric continuity. Some free parameter are added to the original blending function of C1 and C2 Blend B and secure to be G1 and G2 Blend B. Finally, the curvature which measures how quickly a tangent line turns on a curve is applied. So, appropriate result of blending curve can be obtained through the observation of the shape which lies within the convex hull of their control points and its curvature value at the start and end points equal to the curvature of the two circular arcs that are being blended.